ANNAPOLIS, Md. — Democratic and Republican critics of Maryland’s troubled health exchange urged state officials on Monday to consider other options to signing up state residents for health care plans.

Rep. John Delaney, a Democrat, formally asked the state’s health secretary for a specific assessment of the idea of switching to the federal health exchange while Maryland’s exchange is being repaired. He wrote in a letter to Dr. Joshua Sharfstein that Maryland could make the switch in whole or in part or on a temporary basis.

Delaney cited recently released data from the White House that indicated 2.1 million people have signed up for private insurance nationally, including more than 1 million through the federal marketplace. The congressman compared that to 18,257 Maryland residents who have been able to enroll, which is 12 percent of the state’s goal of 150,000.

“We have fallen quite far behind the national average and we’re running out of time,” Delaney wrote, adding that he has heard from frustrated and concerned residents throughout his district, which stretches from Garrett County in western Maryland and includes a significant portion of Montgomery County near the nation’s capital.

On Friday, Gov. Martin O’Malley said he would keep the idea of moving to the federal exchange or partnering with other states under consideration.

“Whatever works best to serve the greatest numbers of people most quickly is what we will do,” O’Malley, a Democrat, said at a Friday briefing with Lt. Gov. Anthony Brown.

Meanwhile, Republican David Craig is urging the state to avoid the exchange and divert marketing and outreach resources to promote direct enrollment options through insurance carriers.

“The task before us is how to mitigate this situation so people can get health care, because Maryland citizens are still having trouble with the website.” Craig, the Harford County executive who is running for the GOP’s nomination for governor, said in a statement.

Maryland’s health exchange website has had problems since it opened Oct. 1. While the O’Malley administration has pointed to improvements in recent weeks, problems have continued. The state has had many more enrollments through Medicaid, which boosts the number of people enrolled under the Affordable Care Act in Maryland to 152,892, the O’Malley administration says. O’Malley hopes to enroll a total of 260,000 people by March 31.

The trouble with the website has presented a political challenge for Brown, who is running for the Democratic nomination for governor and played a leading role in promoting health care reform in Maryland, one of 14 states to run its own exchange. One of his rivals for the nomination, Attorney General Doug Gansler, has cited the health exchange problems in questioning Brown’s leadership.

Brown, who appeared with O’Malley during a Friday briefing on the exchange, announced plans for an emergency bill at the start of the legislative session, which begins Wednesday. The measure will seek to enroll between a few hundred and 5,000 people who have been unable to sign up for insurance through no fault of their own due to computer problems. The measure will seek to insure them through the Maryland Health Insurance Program, a separate safety net plan that has served as a high-risk pool for state residents without insurance. It would cover people retroactively to Jan. 1.